In practice, we tried with different integral cutoff values \(c_0 = 0.005, 0.01, 0.05, 0.10\) . We provide further details on sensitivity analysis to \(c_0\)  in Section  of the Supplementary Material. Based on the sensitivity analysis, we recommend using an integral cutoff of \(c_0 = 0.01\) , after standardizing \(y\)  to have variance 1 prior to fitting SAID. As a rough rule of thumb, loosely based on [1]}, one can view
interactions having \(\mbox{PIP}(h_{uv})\in (0.5,0.75)\)  as barely worth a mention in terms of weight of evidence against the null,
\(\mbox{PIP}(h_{uv})\in [0.75,0.95)\)  as weakly to moderately suggestive,
\(\mbox{PIP}(h_{uv})\in [0.95,0.99)\)  as strong evidence, and \(\mbox{PIP}(h_{uv})\ge 0.99\)  as very strong evidence.
